1. Field of the Invention
The invention is directed to the field of electromechanical piezoresistive nanowire arrays, and in particular nanowire arrays fabricated with doped silicon or germanium, doped III-V semiconductors such as GaAs, GaN and InAs systems, and ultra-thin metal films and used for real-time detection of biological and chemical analytes.
2. Description of the Prior Art
Quantification of Piezoresistors
Fundamentally, all strain gauges are designed to convert mechanical motion into an electronic signal. A piezoresistor is basically a device which changes its resistance when strained. The change in resistance is proportional to the strain experienced by the sensor. The strain sensitivity, which is also called the gage factor (GF), is given by:
                    GF        =                                            (                                                Δ                  ⁢                                                                          ⁢                  R                                R                            )                        /                          (                                                Δ                  ⁢                                                                          ⁢                  L                                L                            )                                =                                    (                                                Δ                  ⁢                                                                          ⁢                  R                                R                            )                        ⁢            Strain                                              (        1        )            where R is the resistance, and L the length of the piezoresistor. There are two components of the piezoresistive effect in most materials: (1) the geometric component and (2) the resistivity components.
When a conducting wire is stretched, it becomes longer and thinner. Its resistance increases according to the Ohm's law. A good example of geometric effect is the liquid strain gauge, such as those made of mercury. When compressed, a tube of mercury becomes shorter in length and larger in diameter to maintain a constant volume. The resistance of such a strain gauge is given by
                    R        =                                            ρ              ⁢                                                          ⁢              L                        A                    =                                    ρ              ⁢                                                          ⁢                              L                2                                      V                                              (        2        )            where ρ is the resistivity, A is the cross sectional area, L is the length and V the volume of the strain gauge.
Therefore,
                    GF        =                                            (                                                ⅆ                                                                          ⁢                  R                                R                            )                        /                          (                                                ⅆ                                                                          ⁢                  L                                L                            )                                =          2                                    (        3        )            This means that all liquid gauges have a gauge factor of 2, since essentially all liquid medium is incompressible. Before replaced by solid stage strain gauge instruments, liquid gauges were extensively used in hospitals to monitor the fluctuations in blood pressure.
Metal wires can also be used as strain gauges. Normally metal cannot be treated as incompressible nor is its resistivity constant. The gauge factors can be expressed by following Ohm's law:
                              R          =                      ρ            ⁢                                                  ⁢                          L              /              A                                      ⁢                                  ⁢                                            ⅆ              R                        /            R                    =                                                                      ⅆ                                                                          ⁢                  ρ                                /                ρ                            +                                                ⅆ                                                                          ⁢                  L                                /                L                            -                                                                    ⅆ                                                                                  ⁢                    A                                    /                  A                                ⁢                                                                  ⁢                GF                                      =                                                                                ⅆ                                                                                  ⁢                    R                                    /                  R                                                                      ⅆ                                                                                  ⁢                    L                                    /                  L                                            =                              1                +                                  2                  ⁢                  v                                +                                                                            ⅆ                                                                                          ⁢                      ρ                                        /                    ρ                                                                              ⅆ                                                                                          ⁢                      L                                        /                    L                                                                                                          (        4        )            In the above, v is defined as Poisson's ratio
  -                              ⅆ                                          ⁢          A                /        A                    2        ⁢                              ⅆ                                                  ⁢            L                    /          L                      .  For different metals, this quantity depends on the material mechanical properties as well as the conduction mechanism. In general metals have gauge factors between 2 and 4.
In equation (3) above, the first component of the gauge factor is a pure geometrical mechanism, but piezoresistive sensing usually refers specifically to strain gauges in semiconductors, whose conducting band changes in response to stress. Some doped semiconductors have a gauge factor over 100 times greater than those attributable to geometric changes alone.
Gauge Factor  GF  =                    ⅆ        R            /      R                      ⅆ        L            /      L       TypeGFMetal foil1 to 5Thin-film metal~2Semiconductor 80 to 150Diffused semiconduetor 80 to 200